"Searchability" is correctly formed, although not common. The Google Ngram Viewer shows some minor usage in recent years (the rate of increase seems to grow a bit with the advent of search engines in the 1990s).
The suffix -ability is reasonably productive in modern English, which means that it can be used to form new words. It is used to derive nouns corresponding to adjectives ending in -able that are ultimately derived from verbs (in this case, the verb search). Deriving nouns from other kinds of words is called "nominalization". (A side note: it's not entirely clear to me whether we can say that -ability nouns are derived "from" -able adjectives, or if we should view -ability as a kind of complex suffix used to derive nouns from verbs "in one step" without necessarily going through an intermediate adjective. Perhaps both of these are over-simplified descriptions of the details. But some kind of derivation is definitely involved somehow.)
Making New Words: Morphological Derivation in English, by Robert M. W. Dixon (2014), mentions this pattern, and a few rules of thumb for when -ability is most often used vs. -ableness. Dixon says that -ability is generally only an option when the derived word is understood to refer to some kind of 'potential'. For example, since the word comfortable usually means "giving comfort" rather than "able to be comforted", the usual corresponding nominalization is comfortableness, not *comfortability.
Other -able adjectives that seem to correspond for the most part to nominalizations in -ableness rather than -ability are reasonable, reasonableness; miserable, miserableness; and charitable, charitableness.
(But interestingly, reasonability and charitability, although incredibly rare, do seem to have become a bit more frequent, both in absolute terms and relative to reasonableness and charitableness, in the past century judging from the Google Ngram Viewer. I don't know if that has any significance—I do remember reading somewhere recently, I don't remember where, that -ability became established as a productive nominalizing suffix in English more recently than -able became established as a productive adjective-forming suffix, so it seems possible to me that the use of -ability may still be "on the rise" in a minor way. Also, miserableness, although better than *miserability, is not used very often because the noun misery expresses much the same idea in most contexts.)
Reference about how -ability became productive
While I don't believe it is the same source that I said above that I remembered reading, I came across the following relevant information in A History of English, by Barbara M. H. Strang (2015).
Strang says "-able" was established as a productive suffix for forming adjectives from English verbs by the 1500s, during the period Strang refers to as "III", from 1570-1370 (Strang uses reverse chronological order) (§112). Shortly after period "III", -ability became a productive suffix, as shown by its use on native verb stems in words such as "lovability" (behavior that we don't see for other -ity nominalizations).
Note about the meaning of "searchability" in particular
1006a made a good point in a comment about the meaning of "searchability". It would regularly mean "ability to be searched", not "ability to be searched for", and so we would talk about the "searchability" of e.g. a database, not of a piece of data (like a title). There are some "-able" adjectives and "-ability" nouns that have different semantics, like "reliable/reliability" (meaning "able to be relied on/ability to be relied on") and "dependable/dependability", but those are exceptional, and apparently "reliable" in particular was criticized for this reason in the past:
Use of the word was heavily criticized in the 19th and early 20th centuries, particularly on the grounds that it represented a supposedly irregular formation (although a number of similar formations were already in existence; compare for example available adj. II., dependable adj., dispensable adj., laughable adj.). For a full contemporary discussion see F. Hall On English Adjectives in -able, with special reference to Reliable (1877), and see also the following:
1996 R. W. Burchfield New Fowler's Mod. Eng. Usage (ed. 3) 665 Earlier objection to the word was based on the belief that reliable ought to mean ‘able to rely’ rather than ‘able to be relied on’. As Alford (1864) expressed it: ‘Reliable is hardly legitimate. We do not rely a man, we rely upon a man; so that reliable does duty for rely-upon-able. “Trustworthy” does all the work required.’
(OED)
